Question

So sánh A và B biết A= \(\frac{15^{2015}+1}{15^{2016}+1}\); B= \(\frac{15^{2014}+1}{15^{2015}+1}\)

Giúp mình với ạ :D

Answer 1

( ghi lại đề ) 

Ta có : 

\(15A=\frac{15^{2016}+15}{15^{2016}+1}=\frac{15^{2016}+1+14}{15^{2016}+1}=\frac{15^{2016}+1}{15^{2016}+1}+\frac{14}{15^{2016}+1}=1+\frac{14}{15^{2016}+1}\)

\(15B=\frac{15^{2015}+15}{15^{2015}+1}=\frac{15^{2015}+1+14}{15^{2015}+1}=\frac{15^{2015}+1}{15^{2015}+1}+\frac{14}{15^{2015}+1}=1+\frac{14}{15^{2015}+1}\)

Vì \(\frac{14}{15^{2016}+1}< \frac{14}{15^{2015}+1}\) nên \(1+\frac{14}{15^{2016}+1}< 1+\frac{14}{15^{2015}+1}\) hay \(15A< 15B\)

\(\Rightarrow\)\(A< B\)

Vậy \(A< B\)

Chúc bạn học tốt ~ 

Answer 2

nhan 2 ve voi 15 

Answer 3

15A=(15^2016+15)/15^2016+1

      =(15^2016+1+14)/15^2016+1

      =          1+14/(15^2016+1).

15B=(15^2015+15)/15^2015+1

      =        1+14/(15^2015+1)

Có: 14/(15^2016+1)<14/(15^2015+1)

=> A<B.

Answer 4

Arigatou bạn Phùng Minh Quân nha~~~